BAGHDAD, Iraq (CNN) -- An Iranian opposition group based in Iraq, labeled a terrorist organization by the United States, gets protection from the U.S. military despite Iraqi pressure to leave the country.

The U.S. considers the Mujahedeen-e-Khalq, or MEK, a source of valuable intelligence on Iran.

The group also is credited with helping expose Iran's secret nuclear program through spying on Tehran for decades.

Iranian officials tied the MEK to an explosion in February at a girls school in Zahedan, Iran. (Full story)

The U.S. State Department considers the MEK a terrorist organization -- meaning no American can deal with it; U.S. banks must freeze its assets; and any American giving support to its members is committing a crime.

The U.S. military, though, regularly escorts MEK supply runs between Baghdad and its base, Camp Ashraf.

"The trips for procurement of logistical needs also take place under the control and protection of the MPs," said Mojgan Parsaii, vice president of MEK and leader of Camp Ashraf.

That's because, according to U.S. documents, coalition forces regard MEK as protected people under the Geneva Conventions.

"The coalition remains deeply committed to the security and rights of the protected people of Ashraf," U.S. Maj. Gen. John D. Gardner wrote in March 2006.

The group also enjoys the protection of the International Committee of the Red Cross.

"The ICRC has made clear that the residents of Camp Ashraf must not be deported, expelled or repatriated," according to an ICRC letter.

Despite repeated requests, neither Iran's ambassador in Baghdad nor the U.S. military would comment on MEK, also known as Mojahedin Khalq Organization, or MKO.

The State Department said Friday the Geneva Conventions protections apply only to MEK residents of Camp Ashraf, and the organization as a whole and its members elsewhere are subject to prosecution for terrorist or criminal acts.

"We still regard them as a terrorist organization," former U.S. Ambassador Zalmay Khalilzad said.

When the U.S. invaded Iraq in 2003, Green Berets arrived at Camp Ashraf to find gardens and monuments, along with more than 2,000 well-maintained tanks, armored personnel carriers, artillery, anti-aircraft guns and vehicles.

All 3,800 camp residents were questioned by Americans. No arrests were made, and the camp quickly surrendered under a cease-fire agreement -- an agreement that also guaranteed its safety.

"Everyone's entry to the camp and his departure are controlled by the U.S. military police force," Parsaii said.

The MEK denies it is a terrorist group. Both Iran and the Iraqi government, however, accuse the group of ongoing terrorist attacks, and the Shiite-dominated Iraqi government wants it out.

"We gave this organization a six-month deadline to leave Iraq, and we informed the Red Cross," said Shirwan al-Wa'eli, Iraq's national security minister. "And presumably, our friends the Americans will respect our decision and they will not stay on Iraqi land."

For now, however, the United States continues to protect MEK.

"There are counter-pressures, too," Khalilzad said. "There are people who say, 'No, they should be allowed to stay here.' And as you know, around the world there are people with different views toward them."